Recent experiments have revealed the phase diagram of infinite-layer Nd\(_{1-x}\) Sr\(_x\) NiO\(_2\)  thin films with a SC dome in the range of hole doping concentration \(12\% < \delta < 25\%\)  [1]}, [2]}. To search for superconductivity, we focus on the underdoped region with \(\delta =12.5\%\)  where the main results are shown in Fig. REF . As shown in Fig. REF  a-b, almost all of the electrons live in the Ni layer while the \(R\)  layer becomes nearly empty with extremely low electron density for both \(\varepsilon _0^{R\text{-Ni}}=3.7\)  and \(3.4\) . This is consistent with the experimental observation [3]}, [1]} that electrons are firstly taken out of the \(R\)  electron pocket when doping holes into the system. It may be worth mentioning that while the \(R\)  band becomes nearly empty, the residual electron density remains nonzero, e.g., around \(0.01\)  for \(\varepsilon _0^{R\text{-Ni}}=3.4\) . This is also in agreement with the discovery of the non-negligible contribution from the Nd \(5d\)  electron pocket that reported in recent RIXS measurements at the Ni \(L\) -edge for Sr-doped nickelates [3]}.
